To calculate the present value (or bond value) of the lease payments, we'll treat the payment structure as an annuity due, since payments are made at the beginning of each month.

Key Information:

• Monthly payment: $P = 20,000$
• Number of years: $6$
• Monthly interest rate: $i = \frac{6\%}{12} = 0.5\% = 0.005$
• Total number of payments: $n = 6 \times 12 = 72$

Formula for Present Value of an Annuity Due:

The present value $PV$ of an annuity due is given by the formula:

$PV = P \times \left( \frac{1 - (1 + i)^{-n}}{i} \right) \times (1 + i)$

Where:

• $P$ is the monthly payment
• $i$ is the monthly interest rate
• $n$ is the total number of payments

Step-by-Step Calculation:

1. Substitute the values: $PV = 20,000 \times \left( \frac{1 - (1 + 0.005)^{-72}}{0.005} \right) \times (1 + 0.005)$

2. Calculate $(1 + 0.005)^{-72}$: $(1 + 0.005)^{-72} = 0.7047 \quad (\text{approx})$

3. Plug it into the formula: $PV = 20,000 \times \left( \frac{1 - 0.7047}{0.005} \right) \times 1.005$

4. Simplify the fraction: $\frac{1 - 0.7047}{0.005} = \frac{0.2953}{0.005} = 59.06$

5. Multiply by $20,000$ and adjust for annuity due: $PV = 20,000 \times 59.06 \times 1.005 = 1,186,188 \quad (\text{approx})$

Final Result:

The present value of the lease payments is approximately $1,186,188.

Would you like more details on any of these steps, or have any questions?

Here are some related questions that you might find helpful:

1. How is an annuity due different from an ordinary annuity?
2. What is the effect of changing the interest rate on the present value?
3. How would the value change if payments were made at the end of the month?
4. What formula is used to calculate the future value of an annuity?
5. How do compound interest and simple interest differ in such scenarios?

Tip: When working with financial formulas, ensure that the interest rate period matches the payment frequency to avoid miscalculations.